Confounding: A Big Idea V1 August 1, 2016 www.StatLit.org/pdf/2016-Schield-ASA-Slides.pdf Page 1 2015 StatChat2 V1 1 Milo Schield, Augsburg College Member: International Statistical Institute US Rep: International Statistical Literacy Project Director, W. M. Keck Statistical Literacy Project VP. National Numeracy Network Editor: www.StatLit.org August 1, 2016 www.StatLit.org/pdf/2016-Schield-ASA-Slides.pdf Confounding: A Big Idea V1 2015 StatChat2 2 Core Concepts in Intro Stats McKenzie (2004): Survey of Educators Goodall@RSS (2007) Big Ideas in Statistics Garfield & Ben Zvi (2008): Big Ideas of Statistics Gould-Miller-Peck (2012). Five Big Ideas Blitzstein@Harvard (2013): 10 Big Ideas Stat110 Stigler (2016): Seven pillars of statistical wisdom 2 V1 2015 StatChat2 3 Ambiguity of “Importance” Topic (randomness) or a claim: ME ~ 1/sqrt(n) This paper focuses on claims or relationships having substantial social or cognitive consequences. 3 V1 2015 StatChat2 4 1A: Fallacies 1. Confusion of the inverse: P(A|B) = P(B|A) 2. Conjunction fallacy: P(A&B) > P(A) 3. P(A&B |C) > P(A |B&C): Three-factor fallacy 4. Individual fallacy 5. Ecological fallacy 6. Simpson’s Paradox 4 V1 2015 StatChat2 5 Contributions of Statistics to Human Knowledge . 5 V1 2015 StatChat2 6 #2A: Butterfly Fallacy One should never trust a statistical association generated by an observational study. An unknown or unmeasured confounder – regardless of size (a small as a butterfly) – can nullify or reverse an observed association. 6
Observational data: Smokers are 10 times as likely to develop lung cancer as are non-smokers.
Some statisticians wanted to support the claim that smoking “caused” lung cancer.
Sir Ronald Fisher (1958) noted that “association was not causation” and that there was a difference (factor of two) in smoking preference between fraternal and identical twins.
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Smoking Causes Cancer:Cornfield’s Reply
Cornfield et al (1959) argued that to nullify or reverse the observed association, the relative risk of a confounder must exceed the relative risk of that association.
Fisher never replied.
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“Cornfield's minimum effect size is as important to observational studies as is the use of randomized assignment to experimental studies.” Schield (1999)
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Cornfield Condition for Nullification or Reversal
Schield (1999) based on realistic data
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Confounder Distribution: Simple One-Parameter Model
How to deal with unknown or unmeasured confounders?
Assume: RR of confounders is distributed exponentially with a minimum RR of one and a mean RR of two.
Observational data: Smokers are 10 times as likely to develop lung cancer as are non-smokers.
Some statisticians wanted to support the claim that smoking “caused” lung cancer.
Sir Ronald Fisher (1958) noted that “association was not causation” and that there was a difference (factor of two) in smoking preference between fraternal and identical twins.
Cornfield et al (1959) argued that to nullify or reverse the observed association, the relative risk of a confounder must exceed the relative risk of that association.
Fisher never replied.
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“Cornfield's minimum effect size is as important to observational studies as is the use of randomized assignment to experimental studies.” Schield (1999)
